D₃×C₃⋊D₃×AGL(1,ℤ/9) #72254085

order	5832
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³×C₃

Aliases

Fitting, Sylow	C₃³×3₋¹⁺² ⋊ C₂³
derived	C₃³×C₉ ⋊ C₂³×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃³×C₉	C₂³×C₃
Frattini	C₃	C₃×D₃²×C₃⋊D₃
Fitting	C₃³×3₋¹⁺²	C₂³
socle	C₃⁴	C₂²×C₃×D₃
LCS	G ▷ C₃³×C₉
UCS	C₁

3078 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 18 points:

(4,5,6)(8,9)(10,15,12,17,13,11)(16,18);(2,3)(5,6)(7,8,9)(10,12,13)(11,17,15)(14,18,16);(1,2,3)(11,14)(12,13)(15,18)(16,17)

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((4,5,6)(8,9)(10,15,12,17,13,11)(16,18), (2,3)(5,6)(7,8,9)(10,12,13)(11,17,15)(14,18,16), (1,2,3)(11,14)(12,13)(15,18)(16,17));